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Geometry Regents Exam 0610 Page 1 Part I 2 credits each 1 In the diagram below of circle O, , and Which statement must be true? 1) 3) 2) 4) 2 What is the negation of the statement “I am not going to eat ice cream”? 1) I like ice cream. 2) I am going to eat ice cream. 3) If I eat ice cream, then I like ice cream. 4) If I don’t like ice cream, then I don’t eat ice cream. 3 The diagram below shows a right pentagonal prism. Which statement is always true? 1) 3) 2) 4) . Geometry Regents Exam 0610 4 In isosceles triangle ABC, 1) 2) Page 2 . Which statement will always be true? 3) 4) 5 The rectangle ABCD shown in the diagram below will be reflected across the x-axis. What will not be preserved? 1) slope of 2) parallelism of and 3) length of 4) measure of 6 A right circular cylinder has an altitude of 11 feet and a radius of 5 feet. What is the lateral area, in square feet, of the cylinder, to the nearest tenth? 1) 172.7 3) 345.4 2) 172.8 4) 345.6 7 A transversal intersects two lines. Which condition would always make the two lines parallel? 1) Vertical angles are congruent. 2) Alternate interior angles are congruent. 3) Corresponding angles are supplementary. 4) Same-side interior angles are complementary. 8 If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral could be a 1) rectangle 3) square 2) rhombus 4) trapezoid Geometry Regents Exam 0610 Page 3 9 What is the converse of the statement "If Bob does his homework, then George gets candy"? 1) If George gets candy, then Bob does his homework. 2) Bob does his homework if and only if George gets candy. 3) If George does not get candy, then Bob does not do his homework. 4) If Bob does not do his homework, then George does not get candy. 10 In 1) 2) 3) 4) , , , and . Which statement about the angles of must be true? 11 Given: In which quadrant will the graphs of the given equations intersect? 1) I 3) III 2) II 4) IV 12 Which diagram shows the construction of an equilateral triangle? 1) 3) 4) 2) 13 Line segment AB is tangent to circle O at A. Which type of triangle is always formed when points A, B, and O are connected? Geometry Regents Exam 0610 1) right 2) obtuse Page 4 3) scalene 4) isosceles 14 What is an equation for the circle shown in the graph below? 1) 2) 3) 4) 15 Which transformation can map the letter S onto itself? 1) glide reflection 3) line reflection 2) translation 4) rotation 16 In isosceles trapezoid ABCD, altitude of the trapezoid? 1) 10 3) 15 2) 12 4) 16 . If , , and , what is the length of the 17 In plane P, lines m and n intersect at point A. If line k is perpendicular to line m and line n at point A, then line k is 1) contained in plane P 3) perpendicular to plane P 2) parallel to plane P 4) skew to plane P 18The diagram below shows and . Geometry Regents Exam 0610 Which transformation will move the image of point B? 1) 3) 2) 4) Page 5 onto 19 In the diagram below of circle O, chords . What is 1) 56 2) 36 ? 3) 28 4) 8 such that point D is the image of point A and point E is and intersect at point B, such that and Geometry Regents Exam 0610 Page 6 20 The diagram below shows the construction of a line through point P perpendicular to line m. Which statement is demonstrated by this construction? 1) If a line is parallel to a line that is perpendicular to a third line, then the line is also perpendicular to the third line. 2) The set of points equidistant from the endpoints of a line segment is the perpendicular bisector of the segment. 3) Two lines are perpendicular if they are equidistant from a given point. 4) Two lines are perpendicular if they intersect to form a vertical line. 21 What is the length, to the nearest tenth, of the line segment joining the points 1) 141.4 3) 151.9 2) 150.5 4) 158.1 22 What is the slope of a line perpendicular to the line whose equation is 1) 3) 3 2) 4) 23 In the diagram below of circle O, secant , , and . What is the length of 1) 4.5 2) 7 ? 3) 9 4) 14 intersects circle O at D, secant and ? ? intersects circle O at E, Geometry Regents Exam 0610 Page 7 24 The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is , and the base is 2x. What is the length of the base? 1) 5 3) 12 2) 10 4) 24 1) 2) 5 10 25 In the diagram below of drawn. , is the bisector of , is the bisector of , and is Which statement must be true? 1) 3) 2) 4) 26 In the diagram below of circle O, chords and intersect at E. Which relationship must be true? 1) 2) 3) 4) 27 Two lines are represented by the equations lines be parallel? 1) -12 2) -3 3) 4) 3 12 and . For which value of m will the Geometry Regents Exam 0610 Page 8 28 The coordinates of the vertices of parallelogram ABCD are , , , and slopes of which line segments could be calculated to show that ABCD is a rectangle? 1) and 3) and 2) and 4) and . The Part II 2 credits each 29 Tim is going to paint a wooden sphere that has a diameter of 12 inches. Find the surface area of the sphere, to the nearest square inch. 30 In the diagram below of the perimeter of . , is a midsegment of , , , and . Find Geometry Regents Exam 0610 31 In right , Page 9 and is 12 degrees less than twice 32 Triangle XYZ, shown in the diagram below, is reflected over the line , the image of . . Find . . State the coordinates of Geometry Regents Exam 0610 33 Two lines, and equidistant from both conditions. Page 10 , are parallel and 10 inches apart. Sketch the locus of all points that are and and 7 inches from point R. Label with an X each point that satisfies 34 The base of a pyramid is a rectangle with a width of 6 cm and a length of 8 cm. Find, in centimeters, the height of the pyramid if the volume is . Geometry Regents Exam 0610 Page 11 Part III 4 credits each 35 Given: Quadrilateral ABCD with Prove: , , and diagonal is drawn Geometry Regents Exam 0610 Page 12 36 Find an equation of the line passing through the point equation is . 37 Write an equation of the circle whose diameter [The use of the grid below is optional.] and perpendicular to the line whose has endpoints and . Geometry Regents Exam 0610 38 In the diagram below, quadrilateral STAR is a rhombus with diagonals , , , , , Find SR, RT, and . Page 13 and intersecting at E. , and . Geometry Regents Exam 0610 www.jmap.org 1 ANS: 1 Parallel lines intercept congruent arcs. PTS: 2 ANS: TOP: 3 ANS: TOP: 4 ANS: TOP: 5 ANS: TOP: 6 ANS: 2 REF: 061001ge 2 PTS: 2 Negations 4 PTS: 2 Solids 3 PTS: 2 Isosceles Triangle Theorem 1 PTS: 2 Properties of Transformations 4 STA: G.G.52 REF: 061002ge TOP: Chords STA: G.G.24 REF: 061003ge STA: G.G.10 REF: 061004ge STA: G.G.31 REF: 061005ge STA: G.G.55 PTS: 7 ANS: TOP: 8 ANS: TOP: 9 ANS: TOP: 10 ANS: TOP: 11 ANS: 2 REF: 061006ge 2 PTS: 2 Parallel Lines and Transversals 4 PTS: 2 Trapezoids 1 PTS: 2 Converse 1 PTS: 2 Angle Side Relationship 3 STA: G.G.14 REF: 061007ge TOP: Volume STA: G.G.35 REF: 061008ge STA: G.G.40 REF: 061009ge STA: G.G.26 REF: 061010ge STA: G.G.34 STA: G.G.70 REF: 061012ge TOP: Quadratic-Linear Systems STA: G.G.20 PTS: 2 12 ANS: 1 TOP: Constructions 13 ANS: 1 TOP: Tangents 14 ANS: 4 The radius is 4. PTS: 15 ANS: TOP: 16 ANS: REF: 061011ge PTS: 2 PTS: 2 REF: 061013ge KEY: point of tangency STA: G.G.50 . 2 REF: 061014ge 4 PTS: 2 Identifying Transformations 3 STA: G.G.72 REF: 061015ge TOP: Equations of Circles STA: G.G.56 Geometry Regents Exam 0610 www.jmap.org . PTS: 17 ANS: TOP: 18 ANS: TOP: 19 ANS: 2 REF: 061016ge 3 PTS: 2 Planes 4 PTS: 2 Identifying Transformations 3 STA: G.G.40 REF: 061017ge TOP: Trapezoids STA: G.G.1 REF: 061018ge STA: G.G.56 PTS: KEY: 20 ANS: TOP: 21 ANS: 2 REF: 061019ge inside circle 2 PTS: 2 Constructions 4 STA: G.G.51 TOP: Arcs Determined by Angles REF: 061020ge STA: G.G.19 PTS: 22 ANS: TOP: 23 ANS: 2 REF: 061021ge 2 PTS: 2 Parallel and Perpendicular Lines 2 STA: G.G.67 REF: 061022ge TOP: Distance STA: G.G.62 STA: G.G.53 TOP: Segments Intercepted by Circle PTS: 2 KEY: two secants 24 ANS: 2 REF: 061023ge Geometry Regents Exam 0610 www.jmap.org PTS: 2 REF: 061024ge STA: G.G.48 TOP: Pythagorean Theorem 25 ANS: 4 is also an angle bisector since it intersects the concurrence of and PTS: 2 REF: 061025ge STA: G.G.21 KEY: Centroid, Orthocenter, Incenter and Circumcenter 26 ANS: 2 PTS: 2 KEY: inscribed 27 ANS: 1 REF: 061026GE STA: G.G.51 TOP: Arcs Determined by Angles PTS: 2 REF: 061027ge STA: G.G.63 TOP: Parallel and Perpendicular Lines 28 ANS: 2 Adjacent sides of a rectangle are perpendicular and have opposite and reciprocal slopes. PTS: 2 29 ANS: 452. REF: 061028ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane PTS: 2 30 ANS: 37. Since REF: 061029ge STA: G.G.16 TOP: Volume and Surface Area is a midsegment, . Geometry Regents Exam 0610 www.jmap.org PTS: 2 31 ANS: 34. REF: 061030ge STA: G.G.42 TOP: Midsegments PTS: 2 32 ANS: REF: 061031ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles PTS: 2 KEY: grids 33 ANS: REF: 061032ge STA: G.G.54 TOP: Reflections PTS: 2 34 ANS: REF: 061033ge STA: G.G.22 TOP: Locus REF: 061034ge STA: G.G.13 TOP: Volume 18. PTS: 2 35 ANS: Geometry Regents Exam 0610 www.jmap.org (Reflexive Property); PTS: 4 36 ANS: REF: 061035ge . (CPCTC). STA: G.G.27 TOP: Quadrilateral Proofs STA: G.G.64 TOP: Parallel and Perpendicular Lines . PTS: 4 37 ANS: REF: 061036ge Midpoint: . Distance: PTS: 2 38 ANS: REF: 061037ge . PTS: 6 (SSS); . REF: 061038ge STA: G.G.71 TOP: Equations of Circles . STA: G.G.39 TOP: Special Parallelograms